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Question

12.Vertices仕6, 0), foci ± 4,0)

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Solution

The given vertices of ellipse are (±6,0) and foci are (±4,0) .(1)

Since the vertices are on the x axis, so the equation of the ellipse is represented

as x 2 a 2 + y 2 b 2 =1 ,where x is the major axis.

Vertices of ellipse are represented as ( ±a,0 ) when x is the major axis.(2)

Compare vertices in equation (1) and (2)

a=6

Foci of ellipse are represented as ( ±c,0 ) when x is the major axis. (3)

Compare foci in equation (1) and (3)

c=4

Substitute values of a and c to determine b .Also, c 2 = a 2 b 2

4 2 = 6 2 b 2 b 2 =3616 b = 20

Equation of ellipse is x 2 6 2 + y 2 ( 20 2 ) =1

Therefore, the equation of ellipse with vertices ( ±6,0 ) and foci ( ±4,0 ) is x 2 36 + y 2 20 =1 .


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